Question: Simplify; express your answer in exponential form. Assume $n\neq 0, x\neq 0$. $\dfrac{{n^{-4}x^{-5}}}{{(n^{5}x^{5})^{2}}}$
Solution: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${n^{-4}x^{-5} = n^{-4}x^{-5}}$ On the left, we have ${n^{-4}}$ to the exponent ${1}$ . Now ${-4 \times 1 = -4}$ , so ${n^{-4} = n^{-4}}$ Apply the ideas above to simplify the equation. $\dfrac{{n^{-4}x^{-5}}}{{(n^{5}x^{5})^{2}}} = \dfrac{{n^{-4}x^{-5}}}{{n^{10}x^{10}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{-4}x^{-5}}}{{n^{10}x^{10}}} = \dfrac{{n^{-4}}}{{n^{10}}} \cdot \dfrac{{x^{-5}}}{{x^{10}}} = n^{{-4} - {10}} \cdot x^{{-5} - {10}} = n^{-14}x^{-15}$